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Консультация № 200516
28.03.2021, 13:13
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос: интегрирование тригонометрической функции ∫dx/(5 cosx +10 sin x)
Обсуждение
28.03.2021, 13:36
общий
28.03.2021, 16:05
Адресаты:
Такие интегралы вычисляют, используя подстановку 
Вы пробовали сделать это?
Решение находится по этой ссылке: Ссылка >> (в появившемся окне нажмите кнопку "=" или нажмите на клавишу "Enter").
Вы пробовали сделать это?Решение находится по этой ссылке: Ссылка >> (в появившемся окне нажмите кнопку "=" или нажмите на клавишу "Enter").
Об авторе:
Facta loquuntur.
Facta loquuntur.
28.03.2021, 13:44
общий
Адресаты:
Можете воспользоваться также этим калькулятором: Ссылка >>
Об авторе:
Facta loquuntur.
Facta loquuntur.
28.03.2021, 15:57
общий
это ответ
Здравствуйте, Фёдор Сергеевич!
Помимо использования универсальной тригонометрической подстановки, решить задачу можно, приведя знаменатель подынтегральной функции к логарифмическому виду, то есть применив формулу вспомогательного угла, известную из тригонометрии:
где
В Вашем случае
Литература
Орловский Д. Г. Неопределённый интеграл. Практикум: Учебное пособие. -- СПб., Лань, 2006. -- 432 с.
Помимо использования универсальной тригонометрической подстановки, решить задачу можно, приведя знаменатель подынтегральной функции к логарифмическому виду, то есть применив формулу вспомогательного угла, известную из тригонометрии:
где
В Вашем случае
Литература
Орловский Д. Г. Неопределённый интеграл. Практикум: Учебное пособие. -- СПб., Лань, 2006. -- 432 с.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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